The uncertainty in the measurement of the integrated luminosity of the data set has been determined to be \(1.0\%\)  [1]}.
The uncertainties of the track reconstruction and PID efficiencies of charged pions
have been studied by using a control sample of
\(e^+e^- \rightarrow K^+K^-\pi ^+\pi ^-\)  [2]},
resulting in \(1.0\) % per pion for tracking and \(1.0\) % per pion for PID.
The uncertainty on the photon efficiency is estimated as \(1.0\) % per
photon by using a control sample of \(e^+e^- \rightarrow \pi ^+\pi ^-\pi ^0\)  [3]}.
Since the number of photon for mode I and mode II are two and one respectively,
the larger change in the cross section due to shifting the detection efficiency
by \(\pm 2.0\) % for mode I and \(\pm 1.0\) % for mode II in the simultaneous fit
(with both shifts having the same sign), is taken as the systematic uncertainty.
